CA1261929A - Vibrating beam force transducer with angled isolator springs - Google Patents
Vibrating beam force transducer with angled isolator springsInfo
- Publication number
- CA1261929A CA1261929A CA000524773A CA524773A CA1261929A CA 1261929 A CA1261929 A CA 1261929A CA 000524773 A CA000524773 A CA 000524773A CA 524773 A CA524773 A CA 524773A CA 1261929 A CA1261929 A CA 1261929A
- Authority
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- Canada
- Prior art keywords
- isolator
- springs
- mass
- isolation mass
- vibrating member
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired
Links
- 238000002955 isolation Methods 0.000 claims abstract description 32
- 238000006243 chemical reaction Methods 0.000 claims abstract description 28
- 230000033001 locomotion Effects 0.000 claims abstract description 26
- 238000000034 method Methods 0.000 claims description 4
- 230000008878 coupling Effects 0.000 claims 2
- 238000010168 coupling process Methods 0.000 claims 2
- 238000005859 coupling reaction Methods 0.000 claims 2
- 239000000463 material Substances 0.000 claims 1
- 239000002184 metal Substances 0.000 claims 1
- 239000010453 quartz Substances 0.000 claims 1
- VYPSYNLAJGMNEJ-UHFFFAOYSA-N silicon dioxide Inorganic materials O=[Si]=O VYPSYNLAJGMNEJ-UHFFFAOYSA-N 0.000 claims 1
- 230000005484 gravity Effects 0.000 description 10
- 238000010586 diagram Methods 0.000 description 4
- 230000007423 decrease Effects 0.000 description 3
- SVTBMSDMJJWYQN-UHFFFAOYSA-N 2-methylpentane-2,4-diol Chemical compound CC(O)CC(C)(C)O SVTBMSDMJJWYQN-UHFFFAOYSA-N 0.000 description 1
- XUKUURHRXDUEBC-KAYWLYCHSA-N Atorvastatin Chemical compound C=1C=CC=CC=1C1=C(C=2C=CC(F)=CC=2)N(CC[C@@H](O)C[C@@H](O)CC(O)=O)C(C(C)C)=C1C(=O)NC1=CC=CC=C1 XUKUURHRXDUEBC-KAYWLYCHSA-N 0.000 description 1
- 230000001133 acceleration Effects 0.000 description 1
- 238000005452 bending Methods 0.000 description 1
- 230000005540 biological transmission Effects 0.000 description 1
- 230000006835 compression Effects 0.000 description 1
- 238000007906 compression Methods 0.000 description 1
- 238000006073 displacement reaction Methods 0.000 description 1
- 230000003090 exacerbative effect Effects 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
- G01P15/00—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration
- G01P15/02—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration by making use of inertia forces using solid seismic masses
- G01P15/08—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration by making use of inertia forces using solid seismic masses with conversion into electric or magnetic values
- G01P15/097—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration by making use of inertia forces using solid seismic masses with conversion into electric or magnetic values by vibratory elements
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
- G01L1/00—Measuring force or stress, in general
- G01L1/10—Measuring force or stress, in general by measuring variations of frequency of stressed vibrating elements, e.g. of stressed strings
- G01L1/106—Constructional details
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
- Y10S—TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10S73/00—Measuring and testing
- Y10S73/01—Vibration
Landscapes
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Vibration Prevention Devices (AREA)
- Piezo-Electric Or Mechanical Vibrators, Or Delay Or Filter Circuits (AREA)
- Apparatus For Radiation Diagnosis (AREA)
- Percussion Or Vibration Massage (AREA)
- Vehicle Body Suspensions (AREA)
- Cable Accessories (AREA)
- Soft Magnetic Materials (AREA)
- Diaphragms For Electromechanical Transducers (AREA)
Abstract
Title of the Invention: VIBRATING BEAM FORCE TRANSDUCER
WITH ANGLED ISOLATOR SPRINGS
ABSTRACT OF THE DISCLOSURE
An isolation system which prevents energy from being transferred by the vibrating member of a resonator to its end mounts is formed by having isolator springs coupled to respective isolation masses. Each of the isolation masses is connected to a corresponding end mount. Each pair of isolator springs is angled in such a way hat the axes of the isolator springs would intersect at a node located somewhere along the longitudinal axes of the vibrating member. Consequently, the axes of the isolator springs are positioned perpendicularly to loci of motions representing the direction of force and moment reactions produced at the roots of the vibrating member.
WITH ANGLED ISOLATOR SPRINGS
ABSTRACT OF THE DISCLOSURE
An isolation system which prevents energy from being transferred by the vibrating member of a resonator to its end mounts is formed by having isolator springs coupled to respective isolation masses. Each of the isolation masses is connected to a corresponding end mount. Each pair of isolator springs is angled in such a way hat the axes of the isolator springs would intersect at a node located somewhere along the longitudinal axes of the vibrating member. Consequently, the axes of the isolator springs are positioned perpendicularly to loci of motions representing the direction of force and moment reactions produced at the roots of the vibrating member.
Description
-~:6~
Titl~ of the Invention: VIBRATING BEAM FORCE TRANSDUCER
WITH ANGLED ISOLATOR SPRINGS
FIELD OF THE INVENT ON
The present invention relates in general to vibrating ~eam resonators, and more particularly to the isolation system of a vibrating beam resonator.
~RIEF DESCRIPTION OF THE PRIOR ART
A vibrating beam resonator is used in a vibrating beam accelerometer for measuring the acceleration of aircraft or for use in missile applications. A vibra~ing ~eam has a structure which has certain string like properties in that, if tension is put on the vibrating beam, the frequency of vibration is increased.
Conversely, if compression is applied to the vibrating beam, the frequency of the ~ibration decreases in response to the force applied. Hence, by using a vibrating beam resonator, an output can be obtained which is representative of the force applied to the vibrating beam resonator. This output, since it can be measured in a digital ~ormat, can easily be interfaced with the pr~sent-day digital computers7 Also, from this measuremant, th~ v~locity of a vehicle and the distance which the vehicle has tra~eled can easily be ascertained.
However~ in order to maka an accurate determination of the force, it is d~sirable that the vibration ~ra~uency of the vibrating beam be a true and accurate repr~sentation Oe the axial stress applied to it. Yet, since the vibrating beam is connected to mounting means, there is always some energy loss due to the ~act that the mounting means must resist the forces .
, . .
Titl~ of the Invention: VIBRATING BEAM FORCE TRANSDUCER
WITH ANGLED ISOLATOR SPRINGS
FIELD OF THE INVENT ON
The present invention relates in general to vibrating ~eam resonators, and more particularly to the isolation system of a vibrating beam resonator.
~RIEF DESCRIPTION OF THE PRIOR ART
A vibrating beam resonator is used in a vibrating beam accelerometer for measuring the acceleration of aircraft or for use in missile applications. A vibra~ing ~eam has a structure which has certain string like properties in that, if tension is put on the vibrating beam, the frequency of vibration is increased.
Conversely, if compression is applied to the vibrating beam, the frequency of the ~ibration decreases in response to the force applied. Hence, by using a vibrating beam resonator, an output can be obtained which is representative of the force applied to the vibrating beam resonator. This output, since it can be measured in a digital ~ormat, can easily be interfaced with the pr~sent-day digital computers7 Also, from this measuremant, th~ v~locity of a vehicle and the distance which the vehicle has tra~eled can easily be ascertained.
However~ in order to maka an accurate determination of the force, it is d~sirable that the vibration ~ra~uency of the vibrating beam be a true and accurate repr~sentation Oe the axial stress applied to it. Yet, since the vibrating beam is connected to mounting means, there is always some energy loss due to the ~act that the mounting means must resist the forces .
, . .
2~
and moments generated by the vibrating beam. This results in a decrease in the Q factor of the resonator, that is, the ratio of total energy per cycle to the energy lost per cycle. And a decrease in Q means that the frequency stability of the resonator is degraded.
Thus, in order to limit the energy loss in the resonator, a high Q must be maintained.
A prior art isolation mounting system for a resonator is disclosed in U.S. Patent 3,4~0,400, issued to Weisbor~, and assiglled to the assignee of the present application. According to Weisbord, to eliminate the energy loss, the center of gravity o~ the isolator mass, which is secured to the vibrating beam, has to be located at a very precise location along the plane of the longitudinal axis of the vibrating beam. By being so positioned; Weisbord teaches that the axial reactions may be canceled. However, oftentimes the criteria as set forth by Weisbord are difficult to attain. For example, were it desirabls to move the center of gravity of the isolator mass from what was prescribed by Weisbord to a location which is further out from the vibrating beam, an additional amount of weight has to be added to the isolator mass, thereby causing different types of problems because the structure no longer adheres to the set criteria.
BRIEF DESCRIPTION OF THE PRESENT INV~NTION
The present invention achieves a successful resolution of the aforesaid problems by, instead of concentrating on the center of gravity of the isolator mass, looking at the positioning of the isolator spring~, which are used to connect the isolator mass to the mounting means. Tharefore, there is provided more flexibility in terms of the design geometry of the isolation system o~ a resonator.
. . .
Moreover, by using the present invention in conjunction with the teachings of Weisbord, a design of an isolation system for a resonator which eliminates unwanted resonances neax the fundamental frequency of the vibrating beam ~an ~e achieved.
The above-mentioned objects and advantages of the present invention will be more clearly understood when considered in conjunction with the accompanying drawings, in which.
FIG5. lA and lB are prior art resonator structures as set forth in the Weisbord patent;
FIG. 2 shows an expanded three-body diagram of the structure shown in FIG. lA;
FIG. 3 is a view which shows only the major reactiQns of the three-body diagram of FIG. 2;
FIG. 4 depic~s the transferring of reactions to the center of gravity of the structure shown in FIG. 3;
FIG. 5 illustrates an isolator mass which has an overhang added thereto;
FI~. 6 shows an isolator mass-beam vibrating system;
FIG. 7 shows. the force and moment reactions at the root of khe vibrating beam;
FIr-. B depicts the loci of motions in an isolation mass:
FIG. 9 shows an isolation system of the present invention, FIG. 10 shows a completely tuned A-frame resonator design; and FIG. 11 is an alternate embodiment of the isolation system o~ the present invention.
DETAILED DESCRIPTION OF'rHE INVENTION
P~eferring now to FIG. 1, there i5 shown a vibrating beam structure as disclosed in the Weisbord patent mentioned hereinabove. For the sake of clarity, only half of the structure designated as 2 is depicted.
In particular, a vibrating beam 4 is connected to an isolator mass 6, which includes two legs 6a and 6b straddling vibratinq beam 4. Structure 2 further includes an end mount 8 and a pair of parallel isolator springs 10 and 12. Isolator mass 6 is coupled at a base 14 to the pair o~ parallel isolator springs, which are in turn connected to end mount 8. As was mentioned in the Weisbord patent, the purpose of the geometry design as shown in FIG. lA is tG maintain the Q factor as high as possible so that the reaction ~orces of the vibrating beam, that is the bending moment M and the shear reaction Y, which are generated at the root of the vibrating beam, designated as 16, would not be transmitted to end mount 8. In other words, the isolator springs and the isolator mass are used ~o prevent energy losses from the vibrating beam. Of course, it should be appreciated that beam 4 is caused to vibrate by an electronic oscillator circuit, which is conventionally known and thus is not shown.
By design, the combination o~ isolator mass 6 and lsolator springs 10 and 12 would have a very low natural frequency, that is when compared to the frequenry of the vibratiny beam~ For example, the vibrating beam typically vibrates at a frequency o~ 40 K Hz~ yet the natural frequency o~ the isolation systPm o~ the resonator is only approximately 5-6 K Hæ. The di~ference of the frequencies between the vibrating beam and the isolator system helps to reduce the shear reaction at root 16 o~ vibrating beam 4. ~owever, in addition to the shear reaction, there i5 generated at root 16 a moment reaction M, which is an angular reactlon that tries to "
induce angular moment in isolator mass 6, where it i5 resisted by axial forces generated in isolator springs lo and 12.
In FI~. lB, the resonator structure shown in ~IG. lA, which is at the rest position, is shown to be maximally deflacted.
FIG. 2 shows an expanded free body diagram which shows all the moment, shear and force reactions present in the structure of FIG. lB. The moments are designated by M, the shear reactions are designated by V and the axial reactions are designated by Fo As shown, the center of gravity C.G. and the beam root are separated by a distance r. As FIG. 2 illustrates only half of a resonator structure, the length of vibrating beam 4 is designated as LB~2. Using the assumptions that the shear and moment reactions of isolator springs 10 and 12 are negligibly small compared to the inertial reactions of the isolator mass at the beam frequency, the axial reaction of vibrating beam 4 is negligible and the axial reactions of isolator ~prings 10 and 12 are also negligibly small, isolator mass 6 of FIG. 2 can be reduced to that shown in FIG~ 3.
By incorporating all of the reactions to the center of yravity C . G . of isolator mass 6, the structure of FIG. 3 can be further reduced to that shown in FIG. 4 wh rein a net moment ~B-rV~ is shown. Setting MB-rVB=O
and utilizing the relationship o~ MB and VB, per the disclosure o~ Weisbord, it can be shown that r=0.215 ~B
This is ~he condition of per~ect tuning ~or the beam structure ~hown in FIG. 1. ~rom this, it is clear that the Weisbord patent teaches that the center of gravity of the isolator mass has to be placed at a very sp~cific lo ation in order to produce an isolation system which uses inertial reactions to cancel moment reactions generated at the root o~ a vibrating beam.
~ owever, .the criteria which was set forth by Weisbord is difficult to meet. For example, if it i5 desirable to move the center of gravity C.G. out to a distance X which exceeds tha limit proposed by Weisbord ~L/6 to L/4), a large overhang 20 needs-to be added to isolator mass 6. See FIG. 5. By adding overhang 20, a lot of additional weight will be added to the isolator mass. This additional weight would cause different problems such as, for instance, the fact that the isolator mass itself may have a freguency which becomes close to the frequency of the vibrating beam, thereby exacerbating the shear reactions. Also, if there is any mistuning, due either to linear displacement of the isolator mass or due to angular motion of the isolator mass, there will be some transmission of beam root moment and shear reactions to the mount. For example, if the isolator system is not per~ectly tuned, i.e. MB ~ rVB, the isolating mass would try to rotate and thereby causes an axial reaction Fs to occur to isolator springs. Sea FIG. 2. It can be shown that the resultant end mount moment react.ion ~R i5 a result of both isolator spring and inertial reactions by the conventional transmissibility equation.
A mistuned isolator mass-vibrating beam system having an angular motion ~I and a linear motion YI is shown in FIG. 6. As was discussed previously, linear motion YI can be taXen care of by the teachings of WeisbordO However, angular motion ~I remains a problem.
Yet, because of the combined linear and angular motions, node points 22 and ~4 are formed along the longitudinal axis of the isolator mass-vibrating beam system. It can easily be shown that the structura of FIG. 6 can be ~xpanded into the free body diagram of FI~. 7, wherein thP moment and shear reactions, as well as the distance dN between the center of gravity C.G. of the isolator , . , ~ 3 mass and khe node, for this instance 22, are shown. For the sake o~ clarity, again only half of the structuré of FIG. ~ i~ illustrated in ~IG. 7.
By utilizing basic linear and angular motion equations, in conjunction with FIG. 6, it can be shown that the following equations represent the linear motion YI and the angular motion ~, respectively I M W 2- (lj M - rV
_~ = ~ (2) where VB = the shear reaction of the vibratiny beam MI = mass of the isolator mass WB = natural frequency of the vibrating beam.
From FIGS. 6 and 7, it. can be seen that the relationship between BN, YI and ~I is as follows:
y N ~I (3) After substituting Equations 1 and 2 into 3, an equation which represents the distance betwee~ a node and the centex of gravity of the isolator mass is as follows:
R 2 (4) d = - ..
(V ~ r) At this point, it should be appreciated that, if MB/VB=r, then dN=~. This is the perfectly tuned Weisbord condition wherein the two isolator springs are positioned in parallel to each other.
Referring now to FIG. 8, there is shown in isolator mass 26 junction points A and B whereby isolator springs are to be attached. Due to the~combined linear and angular motions, respactive loci of points shown as lines 28 and 30 are formed and pass through points A and B, re~pectively. These lines, as shown, are angled, with respect to the X and Y axes. It should be noted that isolator mass 26 would be oriented in the position as shown by the dotted isolator mass 26b, were the isolator mass perfectly tuned as was in the case of the Weisbord structure. It should further be noted that i~ isolator mass 26 is oriented at the position as indicated by isolator mass 26b, then loci 28 and 30 would be oriented in the Y direction, with ref erence to the X and Y axes.
Returning now to isolator mass 2 6 as positioned by the solid line, it can readily be seen that loci 28 and 30 are positioned such that if imaginary lines 28i and 30i, respectively, are drawn from corresponding points A and B
to node 32, loci of motions 28 and 30 are oriented perpendicularly to node 32.
Utilizing the idea that were the isolator springs coupled to the isolator mass at the junction indicated by points A and B in such a way that they would be intersecting at a node which previously had been determined by the above-mentioned equations, it can easily be seen that the isolator springs are called upon to move in their most compliant direction; that is, i~
the isolator spxings are coupled to isolator mass 26 at points A and B so that the de~lection causes the least reaction, the axis o~ the isolator springs will be normal to a direction of motion and will meet at the node.
Thus, the angles of the isolator springs have to be oriented in such a way that the r~spective axis of the isolator springs would be perpen3icular to the corresponding locus of movement at points A and B. This :
angling of the isolator springs from an isolator mass is shown in FIG. 9.
Discussing only 1:he lefl: portion of the structure o~ FIG. 9, it is shown that isolator mass 40 is coupled to end mount 38 by means of isolator springs 34 and 36.
As shown, the axes of isolator springs 34 and 36, represented by dotted lines 34i and 36i, respectively, intersect at node 32. Moreover, these axes 34i and 36i are normal to loci of motion 28 and 30, respectively.
Of course, it should be appreciated that the isolator sprin.gs are offset from planes parallel to the longitudinal axis of the vi~rating beam by an angle ~A~ as illustrated with respect to isolator spring 34.
Although node 32 .is shown to reside within end mount 38 in the structure of FIG. 9, it should be appreciated that the node where tha axis of isolator springs intersect does not necessarily have to reside within the end mount. For example, as shown in FIG. 10, nod~. ~2 is located ou~side o~ end mount 44. This is due to the fact that the structure o~ FIG. 10 has a different geometry than that shown in FIG. 9. Consequently, the loci of motion 46 and 48 o~ the FIG. 10 stxucture, which we shall oall the A-frame resonator, are located at different locations on isolator mass 50. Accordingly, even though the axes of isolator springs 52 and 54 are perpendicular to loci of motion 4~ and 48, re pectively, they intersect node 42 at a point outside of end mount 44. It necessarily follows that the angle 9A of the A-frame resonator is smaller than that of the same for the structure shown in FI~. 9. It should also be emohasized that tha node, instead o~ situa~ing, for example to the le~t of end mount 44, may actually be situated to the right theraof. This is demonstrated in FIG. 11.
As drawn, FIG. 11 shows an alternate design of the isolation system for a vibrating bea~ resona~or. As shown, axes 56i and 58i of isolator springs 56 and 58, respectively, intersect node 64 at a position which is located within isolator mass 62. This is due to the fact that the geometry o~ isolator mass 62 is quite different from those of the earlier figures. Consequently, instead of intersecting at a node ~ocated to the left of base 64 o~ end mount 60, th~ axes of the isolator springs intersect at a node located to the right of base 66 of isolator mass 62. Thus, it should be appreciated that the isol.ator springs can be angled in both directions, that is projecting obliquely toward the end mount or projecting obliquely toward the isolator mass.
I Although the present invention discloses a new isolator design and a new method for bringing about this design, it should be emphasiæed that a combination of the present invention with that which was disclosPd by WPisbord is feasible. For example, it may ke much easier, in a manufacturing process, to adjust both the location o~ the center of gravity of an isolation mass and the angle of the isolator springs than to adjust only ( one of them.
While a preferred embodiment of the invention is disclosed herein for purposes of explanation, numerous changes, modifications, variations, substitutions and equivalents, in whole or in part, will now ~e apparent to those sXilled in the art to which the invention pertains. Accordingly, it is intended that the invention be limited anly by the spixit and scope of the appended claims.
:
and moments generated by the vibrating beam. This results in a decrease in the Q factor of the resonator, that is, the ratio of total energy per cycle to the energy lost per cycle. And a decrease in Q means that the frequency stability of the resonator is degraded.
Thus, in order to limit the energy loss in the resonator, a high Q must be maintained.
A prior art isolation mounting system for a resonator is disclosed in U.S. Patent 3,4~0,400, issued to Weisbor~, and assiglled to the assignee of the present application. According to Weisbord, to eliminate the energy loss, the center of gravity o~ the isolator mass, which is secured to the vibrating beam, has to be located at a very precise location along the plane of the longitudinal axis of the vibrating beam. By being so positioned; Weisbord teaches that the axial reactions may be canceled. However, oftentimes the criteria as set forth by Weisbord are difficult to attain. For example, were it desirabls to move the center of gravity of the isolator mass from what was prescribed by Weisbord to a location which is further out from the vibrating beam, an additional amount of weight has to be added to the isolator mass, thereby causing different types of problems because the structure no longer adheres to the set criteria.
BRIEF DESCRIPTION OF THE PRESENT INV~NTION
The present invention achieves a successful resolution of the aforesaid problems by, instead of concentrating on the center of gravity of the isolator mass, looking at the positioning of the isolator spring~, which are used to connect the isolator mass to the mounting means. Tharefore, there is provided more flexibility in terms of the design geometry of the isolation system o~ a resonator.
. . .
Moreover, by using the present invention in conjunction with the teachings of Weisbord, a design of an isolation system for a resonator which eliminates unwanted resonances neax the fundamental frequency of the vibrating beam ~an ~e achieved.
The above-mentioned objects and advantages of the present invention will be more clearly understood when considered in conjunction with the accompanying drawings, in which.
FIG5. lA and lB are prior art resonator structures as set forth in the Weisbord patent;
FIG. 2 shows an expanded three-body diagram of the structure shown in FIG. lA;
FIG. 3 is a view which shows only the major reactiQns of the three-body diagram of FIG. 2;
FIG. 4 depic~s the transferring of reactions to the center of gravity of the structure shown in FIG. 3;
FIG. 5 illustrates an isolator mass which has an overhang added thereto;
FI~. 6 shows an isolator mass-beam vibrating system;
FIG. 7 shows. the force and moment reactions at the root of khe vibrating beam;
FIr-. B depicts the loci of motions in an isolation mass:
FIG. 9 shows an isolation system of the present invention, FIG. 10 shows a completely tuned A-frame resonator design; and FIG. 11 is an alternate embodiment of the isolation system o~ the present invention.
DETAILED DESCRIPTION OF'rHE INVENTION
P~eferring now to FIG. 1, there i5 shown a vibrating beam structure as disclosed in the Weisbord patent mentioned hereinabove. For the sake of clarity, only half of the structure designated as 2 is depicted.
In particular, a vibrating beam 4 is connected to an isolator mass 6, which includes two legs 6a and 6b straddling vibratinq beam 4. Structure 2 further includes an end mount 8 and a pair of parallel isolator springs 10 and 12. Isolator mass 6 is coupled at a base 14 to the pair o~ parallel isolator springs, which are in turn connected to end mount 8. As was mentioned in the Weisbord patent, the purpose of the geometry design as shown in FIG. lA is tG maintain the Q factor as high as possible so that the reaction ~orces of the vibrating beam, that is the bending moment M and the shear reaction Y, which are generated at the root of the vibrating beam, designated as 16, would not be transmitted to end mount 8. In other words, the isolator springs and the isolator mass are used ~o prevent energy losses from the vibrating beam. Of course, it should be appreciated that beam 4 is caused to vibrate by an electronic oscillator circuit, which is conventionally known and thus is not shown.
By design, the combination o~ isolator mass 6 and lsolator springs 10 and 12 would have a very low natural frequency, that is when compared to the frequenry of the vibratiny beam~ For example, the vibrating beam typically vibrates at a frequency o~ 40 K Hz~ yet the natural frequency o~ the isolation systPm o~ the resonator is only approximately 5-6 K Hæ. The di~ference of the frequencies between the vibrating beam and the isolator system helps to reduce the shear reaction at root 16 o~ vibrating beam 4. ~owever, in addition to the shear reaction, there i5 generated at root 16 a moment reaction M, which is an angular reactlon that tries to "
induce angular moment in isolator mass 6, where it i5 resisted by axial forces generated in isolator springs lo and 12.
In FI~. lB, the resonator structure shown in ~IG. lA, which is at the rest position, is shown to be maximally deflacted.
FIG. 2 shows an expanded free body diagram which shows all the moment, shear and force reactions present in the structure of FIG. lB. The moments are designated by M, the shear reactions are designated by V and the axial reactions are designated by Fo As shown, the center of gravity C.G. and the beam root are separated by a distance r. As FIG. 2 illustrates only half of a resonator structure, the length of vibrating beam 4 is designated as LB~2. Using the assumptions that the shear and moment reactions of isolator springs 10 and 12 are negligibly small compared to the inertial reactions of the isolator mass at the beam frequency, the axial reaction of vibrating beam 4 is negligible and the axial reactions of isolator ~prings 10 and 12 are also negligibly small, isolator mass 6 of FIG. 2 can be reduced to that shown in FIG~ 3.
By incorporating all of the reactions to the center of yravity C . G . of isolator mass 6, the structure of FIG. 3 can be further reduced to that shown in FIG. 4 wh rein a net moment ~B-rV~ is shown. Setting MB-rVB=O
and utilizing the relationship o~ MB and VB, per the disclosure o~ Weisbord, it can be shown that r=0.215 ~B
This is ~he condition of per~ect tuning ~or the beam structure ~hown in FIG. 1. ~rom this, it is clear that the Weisbord patent teaches that the center of gravity of the isolator mass has to be placed at a very sp~cific lo ation in order to produce an isolation system which uses inertial reactions to cancel moment reactions generated at the root o~ a vibrating beam.
~ owever, .the criteria which was set forth by Weisbord is difficult to meet. For example, if it i5 desirable to move the center of gravity C.G. out to a distance X which exceeds tha limit proposed by Weisbord ~L/6 to L/4), a large overhang 20 needs-to be added to isolator mass 6. See FIG. 5. By adding overhang 20, a lot of additional weight will be added to the isolator mass. This additional weight would cause different problems such as, for instance, the fact that the isolator mass itself may have a freguency which becomes close to the frequency of the vibrating beam, thereby exacerbating the shear reactions. Also, if there is any mistuning, due either to linear displacement of the isolator mass or due to angular motion of the isolator mass, there will be some transmission of beam root moment and shear reactions to the mount. For example, if the isolator system is not per~ectly tuned, i.e. MB ~ rVB, the isolating mass would try to rotate and thereby causes an axial reaction Fs to occur to isolator springs. Sea FIG. 2. It can be shown that the resultant end mount moment react.ion ~R i5 a result of both isolator spring and inertial reactions by the conventional transmissibility equation.
A mistuned isolator mass-vibrating beam system having an angular motion ~I and a linear motion YI is shown in FIG. 6. As was discussed previously, linear motion YI can be taXen care of by the teachings of WeisbordO However, angular motion ~I remains a problem.
Yet, because of the combined linear and angular motions, node points 22 and ~4 are formed along the longitudinal axis of the isolator mass-vibrating beam system. It can easily be shown that the structura of FIG. 6 can be ~xpanded into the free body diagram of FI~. 7, wherein thP moment and shear reactions, as well as the distance dN between the center of gravity C.G. of the isolator , . , ~ 3 mass and khe node, for this instance 22, are shown. For the sake o~ clarity, again only half of the structuré of FIG. ~ i~ illustrated in ~IG. 7.
By utilizing basic linear and angular motion equations, in conjunction with FIG. 6, it can be shown that the following equations represent the linear motion YI and the angular motion ~, respectively I M W 2- (lj M - rV
_~ = ~ (2) where VB = the shear reaction of the vibratiny beam MI = mass of the isolator mass WB = natural frequency of the vibrating beam.
From FIGS. 6 and 7, it. can be seen that the relationship between BN, YI and ~I is as follows:
y N ~I (3) After substituting Equations 1 and 2 into 3, an equation which represents the distance betwee~ a node and the centex of gravity of the isolator mass is as follows:
R 2 (4) d = - ..
(V ~ r) At this point, it should be appreciated that, if MB/VB=r, then dN=~. This is the perfectly tuned Weisbord condition wherein the two isolator springs are positioned in parallel to each other.
Referring now to FIG. 8, there is shown in isolator mass 26 junction points A and B whereby isolator springs are to be attached. Due to the~combined linear and angular motions, respactive loci of points shown as lines 28 and 30 are formed and pass through points A and B, re~pectively. These lines, as shown, are angled, with respect to the X and Y axes. It should be noted that isolator mass 26 would be oriented in the position as shown by the dotted isolator mass 26b, were the isolator mass perfectly tuned as was in the case of the Weisbord structure. It should further be noted that i~ isolator mass 26 is oriented at the position as indicated by isolator mass 26b, then loci 28 and 30 would be oriented in the Y direction, with ref erence to the X and Y axes.
Returning now to isolator mass 2 6 as positioned by the solid line, it can readily be seen that loci 28 and 30 are positioned such that if imaginary lines 28i and 30i, respectively, are drawn from corresponding points A and B
to node 32, loci of motions 28 and 30 are oriented perpendicularly to node 32.
Utilizing the idea that were the isolator springs coupled to the isolator mass at the junction indicated by points A and B in such a way that they would be intersecting at a node which previously had been determined by the above-mentioned equations, it can easily be seen that the isolator springs are called upon to move in their most compliant direction; that is, i~
the isolator spxings are coupled to isolator mass 26 at points A and B so that the de~lection causes the least reaction, the axis o~ the isolator springs will be normal to a direction of motion and will meet at the node.
Thus, the angles of the isolator springs have to be oriented in such a way that the r~spective axis of the isolator springs would be perpen3icular to the corresponding locus of movement at points A and B. This :
angling of the isolator springs from an isolator mass is shown in FIG. 9.
Discussing only 1:he lefl: portion of the structure o~ FIG. 9, it is shown that isolator mass 40 is coupled to end mount 38 by means of isolator springs 34 and 36.
As shown, the axes of isolator springs 34 and 36, represented by dotted lines 34i and 36i, respectively, intersect at node 32. Moreover, these axes 34i and 36i are normal to loci of motion 28 and 30, respectively.
Of course, it should be appreciated that the isolator sprin.gs are offset from planes parallel to the longitudinal axis of the vi~rating beam by an angle ~A~ as illustrated with respect to isolator spring 34.
Although node 32 .is shown to reside within end mount 38 in the structure of FIG. 9, it should be appreciated that the node where tha axis of isolator springs intersect does not necessarily have to reside within the end mount. For example, as shown in FIG. 10, nod~. ~2 is located ou~side o~ end mount 44. This is due to the fact that the structure o~ FIG. 10 has a different geometry than that shown in FIG. 9. Consequently, the loci of motion 46 and 48 o~ the FIG. 10 stxucture, which we shall oall the A-frame resonator, are located at different locations on isolator mass 50. Accordingly, even though the axes of isolator springs 52 and 54 are perpendicular to loci of motion 4~ and 48, re pectively, they intersect node 42 at a point outside of end mount 44. It necessarily follows that the angle 9A of the A-frame resonator is smaller than that of the same for the structure shown in FI~. 9. It should also be emohasized that tha node, instead o~ situa~ing, for example to the le~t of end mount 44, may actually be situated to the right theraof. This is demonstrated in FIG. 11.
As drawn, FIG. 11 shows an alternate design of the isolation system for a vibrating bea~ resona~or. As shown, axes 56i and 58i of isolator springs 56 and 58, respectively, intersect node 64 at a position which is located within isolator mass 62. This is due to the fact that the geometry o~ isolator mass 62 is quite different from those of the earlier figures. Consequently, instead of intersecting at a node ~ocated to the left of base 64 o~ end mount 60, th~ axes of the isolator springs intersect at a node located to the right of base 66 of isolator mass 62. Thus, it should be appreciated that the isol.ator springs can be angled in both directions, that is projecting obliquely toward the end mount or projecting obliquely toward the isolator mass.
I Although the present invention discloses a new isolator design and a new method for bringing about this design, it should be emphasiæed that a combination of the present invention with that which was disclosPd by WPisbord is feasible. For example, it may ke much easier, in a manufacturing process, to adjust both the location o~ the center of gravity of an isolation mass and the angle of the isolator springs than to adjust only ( one of them.
While a preferred embodiment of the invention is disclosed herein for purposes of explanation, numerous changes, modifications, variations, substitutions and equivalents, in whole or in part, will now ~e apparent to those sXilled in the art to which the invention pertains. Accordingly, it is intended that the invention be limited anly by the spixit and scope of the appended claims.
:
Claims (11)
1. An apparatus comprising:
a member adapted to vibrate in a plane along the longitudinal axis;
means connected to the member for maintaining the vibration of the member at a characteristic frequency;
an isolation mass secured to each end of the member, each isolation mass including a base extending transversely from the longitudinal axis in both directions;
an end mount positioned in parallel spaced relation to the base of each isolation mass;
a pair of non-parallel spaced isolator springs coupling each isolation mass to the corresponding end mount, each isolator spring being positioned perpendicularly to a locus of motion located proximately at the base of the isolation mass, the locus of motion intersecting the junction of the base where the isolation spring is coupled to the isolation mass, the locus of motion being representative of the direction of motion of the force and moment reactions produced at the root of the vibrating member:
whereby energy losses from the vibrating member are substantially eliminated.
a member adapted to vibrate in a plane along the longitudinal axis;
means connected to the member for maintaining the vibration of the member at a characteristic frequency;
an isolation mass secured to each end of the member, each isolation mass including a base extending transversely from the longitudinal axis in both directions;
an end mount positioned in parallel spaced relation to the base of each isolation mass;
a pair of non-parallel spaced isolator springs coupling each isolation mass to the corresponding end mount, each isolator spring being positioned perpendicularly to a locus of motion located proximately at the base of the isolation mass, the locus of motion intersecting the junction of the base where the isolation spring is coupled to the isolation mass, the locus of motion being representative of the direction of motion of the force and moment reactions produced at the root of the vibrating member:
whereby energy losses from the vibrating member are substantially eliminated.
2. The apparatus according to claim 1, wherein each non-parallel spaced isolator spring is angled obliquely toward the longitudinal axis from the base of the isolation mass to the corresponding end mount, respective axes of the isolator springs intersecting at a node located in the direction away from the vibrating member and the junction where the springs are coupled to the base.
3. The apparatus according to claim 1, wherein each non-parallel spaced isolator spring is angled obliquely toward the longitudinal axis from the corresponding end mount to the base of the isolation mass, the axes of the isolator springs intersecting at a node located away from the junction of the isolator mass where the springs are coupled.
4. The apparatus according to claim 2, wherein the member is a beam.
5. The apparatus according to claim 3, wherein the member is a beam.
6. The apparatus according to claim 1, wherein the apparatus is made of piezoelectric material.
7. The apparatus according to claim 1, wherein the apparatus is made of quartz.
8. The apparatus according to claim 1, wherein the apparatus is made of metal.
9. In an apparatus including a vibrating member, an isolation mass secured to each end of the vibrating member and an end mount positioned in spaced relation to each isolation mass, a method of preventing energy losses from the vibrating member, comprising:
interposing between each isolation mass and the corresponding end mount a pair of non-parallel spaced isolator springs for coupling the isolation mass to the corresponding end mount;
positioning each isolator spring perpendicularly to a locus of motion located in the isolation mass, the locus of motion intersecting the junction where the isolator spring is coupled to the isolation mass, the locus of motion being representative of the direction of motion of the force and moment reactions produced at the root of the vibrating member;
thereby preventing energy losses from the vibrating member.
interposing between each isolation mass and the corresponding end mount a pair of non-parallel spaced isolator springs for coupling the isolation mass to the corresponding end mount;
positioning each isolator spring perpendicularly to a locus of motion located in the isolation mass, the locus of motion intersecting the junction where the isolator spring is coupled to the isolation mass, the locus of motion being representative of the direction of motion of the force and moment reactions produced at the root of the vibrating member;
thereby preventing energy losses from the vibrating member.
10. The method according to claim 9, wherein the positioning step further comprises:
angling each isolator spring obliquely from the base of the isolation mass to the corresponding end mount; and projecting the axes of the isolator springs toward the longitudinal axis of the vibrating member;
thereby intersecting the node located in the direction away from the vibrating member and the junctions of the isolation mass where the isolator springs are coupled.
angling each isolator spring obliquely from the base of the isolation mass to the corresponding end mount; and projecting the axes of the isolator springs toward the longitudinal axis of the vibrating member;
thereby intersecting the node located in the direction away from the vibrating member and the junctions of the isolation mass where the isolator springs are coupled.
11. The method according to claim 9, wherein the positioning step further comprises:
angling each isolator spring obliquely from the corresponding end mount to the isolation mass;
projecting the axes of the isolator springs toward the longitudinal axis of the vibrating member;
thereby intersecting a node located away from the junctions of the isolator mass where the springs are coupled.
angling each isolator spring obliquely from the corresponding end mount to the isolation mass;
projecting the axes of the isolator springs toward the longitudinal axis of the vibrating member;
thereby intersecting a node located away from the junctions of the isolator mass where the springs are coupled.
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US841,982 | 1986-03-20 | ||
| US06/841,982 US4658174A (en) | 1986-03-20 | 1986-03-20 | Vibrating beam force transducer with angled isolator springs |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CA1261929A true CA1261929A (en) | 1989-09-26 |
Family
ID=25286247
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA000524773A Expired CA1261929A (en) | 1986-03-20 | 1986-12-08 | Vibrating beam force transducer with angled isolator springs |
Country Status (11)
| Country | Link |
|---|---|
| US (1) | US4658174A (en) |
| JP (1) | JPS62229039A (en) |
| AU (1) | AU6755287A (en) |
| CA (1) | CA1261929A (en) |
| DE (1) | DE3709096A1 (en) |
| FR (1) | FR2596152A1 (en) |
| GB (1) | GB2188149B (en) |
| IL (1) | IL80565A (en) |
| IT (1) | IT1203504B (en) |
| NO (1) | NO864954L (en) |
| SE (1) | SE8700008L (en) |
Families Citing this family (25)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| FR2574209B1 (en) * | 1984-12-04 | 1987-01-30 | Onera (Off Nat Aerospatiale) | RESONATOR WITH VIBRATING BLADE |
| US4743790A (en) * | 1987-04-14 | 1988-05-10 | Crystal Gage Inc. | Force sensing vibrating beam resonator |
| US4766768A (en) | 1987-10-22 | 1988-08-30 | Sundstrand Data Control, Inc. | Accelerometer with isolator for common mode inputs |
| JPH03501410A (en) * | 1988-07-18 | 1991-03-28 | ワース・ガロー・メステクニツク・アクチエンゲゼルシヤフト | Mass and force measuring device with elastic reduction member |
| US4945765A (en) * | 1988-08-31 | 1990-08-07 | Kearfott Guidance & Navigation Corp. | Silicon micromachined accelerometer |
| US5109175A (en) * | 1989-12-21 | 1992-04-28 | Lucas Schaevitz Inc. | Monolithic resonator for vibrating beam force sensors |
| US4980598A (en) * | 1989-12-21 | 1990-12-25 | Lucas Schaevitz Inc. | Monolithic resonator for a vibrating beam accelerometer |
| US5135312A (en) * | 1990-07-20 | 1992-08-04 | Sundstrand Data Control, Inc. | Temperature transducer |
| US5156460A (en) * | 1990-11-05 | 1992-10-20 | Sundstrand Corporation | Crystal temperature transducer |
| WO1993010428A1 (en) * | 1991-11-12 | 1993-05-27 | Masstech Scientific Pty. Ltd. | Force or load sensors |
| US5336854A (en) | 1992-04-03 | 1994-08-09 | Weigh-Tronix, Inc. | Electronic force sensing load cell |
| US5442146A (en) | 1992-04-03 | 1995-08-15 | Weigh-Tronix, Inc. | Counting scale and load cell assembly therefor |
| US5313023A (en) | 1992-04-03 | 1994-05-17 | Weigh-Tronix, Inc. | Load cell |
| US5391844A (en) | 1992-04-03 | 1995-02-21 | Weigh-Tronix Inc | Load cell |
| CH687103A5 (en) * | 1993-08-20 | 1996-09-13 | Mettler Toledo Ag | Flat one-piece measuring string with two knots for displacement or force measurement. |
| FR2723638B1 (en) * | 1994-08-10 | 1996-10-18 | Sagem | FORCE-FREQUENCY TRANSDUCER WITH VIBRATING BEAMS |
| WO1996024853A1 (en) * | 1995-02-09 | 1996-08-15 | Alliedsignal Inc. | Accelerometer with improved support rim isolation |
| JP3119135B2 (en) * | 1995-09-11 | 2000-12-18 | 株式会社村田製作所 | Acceleration sensor |
| DE60142930D1 (en) | 2001-01-17 | 2010-10-07 | Honeywell Int Inc | DOUBLE RESONANT DUCTING CONVERTER WITH REDUCED LONGITUDINAL PUMP |
| US6497152B2 (en) | 2001-02-23 | 2002-12-24 | Paroscientific, Inc. | Method for eliminating output discontinuities in digital pressure transducers and digital pressure transducer employing same |
| US6595054B2 (en) | 2001-05-14 | 2003-07-22 | Paroscientific, Inc. | Digital angular rate and acceleration sensor |
| US20040016307A1 (en) * | 2002-07-24 | 2004-01-29 | Albert William C. | Vibration isolation mechanism for a vibrating beam force sensor |
| US6826960B2 (en) | 2002-08-07 | 2004-12-07 | Quartz Sensors, Inc. | Triaxial acceleration sensor |
| US7250705B2 (en) * | 2005-09-16 | 2007-07-31 | Texas Instruments Incorporated | Resonant oscillating device actuator structure |
| US11474126B2 (en) | 2020-03-05 | 2022-10-18 | Quartz Seismic Sensors, Inc. | High precision rotation sensor and method |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US3238789A (en) * | 1961-07-14 | 1966-03-08 | Litton Systems Inc | Vibrating bar transducer |
| US3269192A (en) * | 1962-11-07 | 1966-08-30 | Gen Precision Inc | Tuning fork digital accelerometer |
| US3440888A (en) * | 1962-11-07 | 1969-04-29 | Gen Precision Systems Inc | Bifurcate resonance column |
| US3413859A (en) * | 1965-01-04 | 1968-12-03 | Gen Precision Systems Inc | Digital rate gyro |
| US3486383A (en) * | 1965-01-04 | 1969-12-30 | Singer General Precision | Vibrating beam transducer |
| US3465597A (en) * | 1965-05-25 | 1969-09-09 | Singer General Precision | Vibrating-column accelerometer |
| US3505866A (en) * | 1966-10-13 | 1970-04-14 | Singer General Precision | Single tine digital force transducer |
| US3399572A (en) * | 1966-12-01 | 1968-09-03 | Gen Precision Inc | Vibrating beam pressure transducer |
| US3479536A (en) * | 1967-03-14 | 1969-11-18 | Singer General Precision | Piezoelectric force transducer |
| US3470400A (en) * | 1967-12-21 | 1969-09-30 | Singer General Precision | Single beam force transducer with integral mounting isolation |
| US3766616A (en) * | 1972-03-22 | 1973-10-23 | Statek Corp | Microresonator packaging and tuning |
| US4104920A (en) * | 1977-04-01 | 1978-08-08 | The Singer Company | Piezoelectric damping mechanism |
| US4221131A (en) * | 1979-05-29 | 1980-09-09 | The Singer Company | Vibrating beam accelerometer |
| US4321500A (en) * | 1979-12-17 | 1982-03-23 | Paroscientific, Inc. | Longitudinal isolation system for flexurally vibrating force transducers |
| FR2477803A1 (en) * | 1980-03-04 | 1981-09-11 | Suwa Seikosha Kk | QUARTZ RESONATOR TYPE DIAPASON TYPE COUPLING |
| US4445065A (en) * | 1981-09-14 | 1984-04-24 | The Singer Company | Non-prismal beam resonator |
| US4446394A (en) * | 1981-09-14 | 1984-05-01 | The Singer Company | Linearizing mechanism for a vibrating beam force transducer |
| GB2115551B (en) * | 1982-02-09 | 1985-11-13 | Itt Ind Ltd | Load sensor |
| JPS5936919A (en) * | 1982-08-25 | 1984-02-29 | 三菱鉱業セメント株式会社 | Porcelain condenser |
| JPS6010122A (en) * | 1983-06-30 | 1985-01-19 | Shinko Denshi Kk | Load converting mechanism |
-
1986
- 1986-03-20 US US06/841,982 patent/US4658174A/en not_active Expired - Lifetime
- 1986-11-10 IL IL80565A patent/IL80565A/en not_active IP Right Cessation
- 1986-11-20 GB GB8627717A patent/GB2188149B/en not_active Expired - Fee Related
- 1986-12-05 FR FR8617078A patent/FR2596152A1/en active Pending
- 1986-12-08 CA CA000524773A patent/CA1261929A/en not_active Expired
- 1986-12-09 NO NO864954A patent/NO864954L/en unknown
- 1986-12-25 JP JP61308092A patent/JPS62229039A/en active Pending
-
1987
- 1987-01-02 SE SE8700008A patent/SE8700008L/en not_active Application Discontinuation
- 1987-01-14 AU AU67552/87A patent/AU6755287A/en not_active Abandoned
- 1987-02-25 IT IT19482/87A patent/IT1203504B/en active
- 1987-03-20 DE DE19873709096 patent/DE3709096A1/en not_active Withdrawn
Also Published As
| Publication number | Publication date |
|---|---|
| IL80565A0 (en) | 1987-02-27 |
| GB2188149B (en) | 1990-05-02 |
| FR2596152A1 (en) | 1987-09-25 |
| IT8719482A0 (en) | 1987-02-25 |
| GB2188149A (en) | 1987-09-23 |
| IL80565A (en) | 1990-06-10 |
| IT1203504B (en) | 1989-02-15 |
| JPS62229039A (en) | 1987-10-07 |
| NO864954D0 (en) | 1986-12-09 |
| GB8627717D0 (en) | 1986-12-17 |
| NO864954L (en) | 1987-09-21 |
| AU6755287A (en) | 1987-09-24 |
| DE3709096A1 (en) | 1987-09-24 |
| US4658174A (en) | 1987-04-14 |
| SE8700008D0 (en) | 1987-01-02 |
| SE8700008L (en) | 1987-09-21 |
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